VELOCITY OF REACTION 191 



experimentally, and probably is not so; for as the number of 

 molecules of substratum decreases, there will be continually a larger 

 number of enzyme molecules relatively, and there may be in con- 

 sequence a greater amount of action upon each substratum molecule 

 that is, the value of k on this account will increase throughout the 

 reaction. Thus indirectly k becomes a function of x, the quantity 

 inverted. There is no experimental basis for the assumption that 

 the effect of the enzyme upon each molecule of substratum is the 

 same, no matter what the concentration in substratum; and when 

 the concentration of the substratum falls in the course of the reac- 

 tion, then the available material upon which the enzyme acts being 

 >ned, the effect upon each molecule must be increased. There- 

 fore although the velocity of change diminishes as the mass action 

 law indicates, on account of the diminution in unchanged material, 

 there is a factor of increase on account of greater activity being 

 exercised by the constant number of enzyme molecules upon each 

 of the now smaller number of substratum molecules. 1 A second 



dx 



assumption which is made in applying the law ^j=k (ax) to 



enzymic action has already been alluded to in the derivation of the 

 equation (see p. 52), viz., that the action is taken to be irreversible, 

 or that the tendency to reversion may be neglected. 



This assumption is in all probability not experimentally justi- 

 fiable, especially at the later stages of the reaction. For it does 

 not follow that, because a reaction runs practically to completion 

 as, for example, that induced by invertase upon cane-sugar 

 therefore the effect of the tendency to reversion in decreasing the 

 velocity of reaction in the late stages can be neglected. 



The same causes which produce the actual reversibility seen 

 in the case of strong solutions must be present in dilute solutions, 

 and emphasis must be laid upon the fact that, on either side of 

 the equilibrium point for some distance, the tendency for the reac- 



1 A kinetic analogy may make the contention clearer. Suppose the 

 enzyme molecules are a fleet of battleships, firing at a number of targets 

 which are gradually sunk as a result. Then, as the targets sink, the rate of 

 disappearance will decrease, and provided the number of targets is large 

 enough the rate \\ ill be proportional to the number at any instant that is, 



the law i f k (a - .r) will hold. As the firing goes on, however, there will 



come in a factor of increase in the rate of sinking, because each target will be 

 attacked by an increased number of ships. 



